已知 tanθ和tan(4/π-θ)是方程x²+px+q=0的两个根,且有tanθ:tan(4/π-θ)=3:2,求p与q的值.

根据韦达定理有：tanθ+tan(π/4-θ)=-p (1)tanθ*tan(π/4-θ)=q (2)tanθ:tan(π/4-θ)=3:22tanθ=3(1-tanθ)/(1+tanθ)2tan²θ+5tanθ-3=0tanθ=1/2 或 tanθ=-3tan(π/4-θ)=(1-tanθ)/(1+tanθ)tan(π/4-...